The Supreme Court had last month upheld the Constitutional validity of Aadhaar, the 12-digit biometric based unique identity number, but restricted its use by private entities like telecom operators for verifying identity of mobile phone user.
Jaitley, while addressing Hindustan Times Leadership Summit, said by law it can still be done, provided it is done under the adequate provision.
Jaitley hailed the Supreme Court verdict upholding the validity of Aadhaar and termed it a "very sound judgment".
The finance ministry said the Supreme Court has upheld most of what Aadhaar does.
"What had not been upheld falls in two categories. One is the principle of proportionality that Aadhaar will help in these cases and then do it by an appropriate law.
"So the whole argument which was given that private companies can't use it, there is Section 57 which says you can authorise others either by law or contract. So what has been struck down is by contract," Jaitley said.
"By law it can still be done, provided you do it under the adequate provision of law and do it on the basis of that in this field it is necessary," he said.
Jaitley said the Supreme Court has permitted Aadhaar linkage in several areas like income tax, based on "the principle of proportionality".
"If you are able to show the kind of data that in mobile telephony it (Aadhaar linkage) will help, it can happen. So mobile and bank accounts are two critical areas," he said.
Jaitley, however, did not say if the government was planning to bring a law in Parliament for the purpose.
Aadhaar would remain mandatory for filing of IT returns and allotment of Permanent Account Number (PAN), it would not be mandatory to link Aadhaar to bank accounts and telecom service providers cannot seek its linking for mobile connections, the Supreme Court had said in a historic verdict.
(With inputs from agencies)